There's another question you can study that has a surprising answer. Suppose you took all possible mono-spectral lights, and computed the three "responses" associated with them. You could call these three responses , and . If for each you plotted the point , , in 3-space, you'd get an arc of points corresponding to wavelengths between 700 nm and 400 nm (which are the longest and shortest wavelengths we can see, more or less). This arc, if you actually drew it, would turn out to have the shape of a horseshoe. (If you turned the lights down a bit, you would get a smaller horseshoe -- closer to the origin -- and if you turned them up, you'd get a larger one. I'm going to assume that all lights in the rest of this discussion are adjusted so that the total stimulus -- r + g + b -- is always the same.)

The horseshoe shape in itself is not surprising. But suppose now that
you have a color monitor that has three "color guns" that can turn on
a certain amount of red, green, or blue at each pixel. Suppose that
the "red" that the first gun turns on is nearly an ideal red -- it's
right at the 700 nm end of the horseshoe. And suppose that the blue is
right at the 400 nm end of the horseshoe, and that the green is right
at the bend of the horseshoe. Then any color you can create by turning
on a combination of these will lie somewhere in the triangle whose
vertices are those three points. It doesn't take much to see that
*some* pure spectral colors cannot be reproduced by your monitor,
even though it's nearly an ideal monitor. In fact, most monitors have
a red that's not really at one end of the horseshoe, and a blue that's
not really at the other, and a green that's not quite at the edge of
the horseshoe, so the "gamut" of screen colors is a relatively small
triangle within the larger "filled-in-horseshoe-shape" gamut of all
possible colors.

Worse still, your printer has the same problem -- it's got various inks that can reflect white light in various ways, but once again, combinations of those inks lead to colors inside some convex polygon inside the horseshoe, and it's probably not the same polygon as your monitor. So if you craft an ideal image on your monitor, it may be ugly when you print it! Those are the grim facts of life about color in the computer graphics world, and they've all been based on the generous assumption that everything in sight is linear, which turns out to be overoptimistic, alas. Illustrations showing the horseshoe shape are under construction, and may appear here at some time in the future...

Questions or feedback on these illustrations should be sent to *John F. Hughes*.

Questions on the Java source should be sent to *Adam Doppelt*.